System and method for sparse touch sensing on capacitive touch screen

ABSTRACT

An embodiment of the invention provides a method of detecting the position(s) where sensor(s) are activated on an interactive screen using sparse-activation compressive sensing. Sparse-activation compressive sensing makes use of the situation where the number of simultaneously activated sensors is substantially smaller than the number of sensors (nodes). Because the number of simultaneously activated sensors is substantially smaller than the number of sensors, the number of measurements required for determining which sensors are activated may also be reduced. Because fewer measurements are required when compared with full-scan techniques, less circuitry and power is required to detect the location(s) of activated sensors on an interactive screen.

BACKGROUND

The popularity of interactive screens has been increasing since the introduction of smart phones and tablet PCs (personal computers). Interactive screens are becoming larger in size, and there is an increasing demand on the responsiveness, resolution and intelligence of these interactive screens. Generally, an interactive screen functions by scanning each sensor, often called a node, on the screen periodically to detect the location(s) where the sensor has been activated. A sensor may be activated by direct physical contact by an object (e.g human finger or a stylus), by objects in proximity to a sensor or by stimulating a sensor from a distance.

The number of sensors activated on an interactive screen at a particular time is relatively small when compared to the number of sensors on the interactive screen. FIG. 3 shows an example of the sparse characteristics of contact made with an interactive screen. In the example shown in FIG. 3, capacitance changes on active nodes when fingers are in close proximity with the interactive screen. At locations on the interactive screen where fingers are not in close proximity with the interactive screen, the capacitance does not change.

One method of determining when sensors on an interactive screen are activated is to periodically scan all of the sensors on the screen to monitor which sensors have been activated and which sensors have not been activated. A full scan (i.e. scanning all of the sensors on the screen) may be time consuming and may consume more power than is necessary. Power consumption on portable electronic devices is critical because the amount of power may be limited. The amount of power used to drive an interactive screen may be reduced by reducing the sensing complexity of an interactive screen while maintaining the accuracy of the detection and localization of where sensors are activated.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram showing a cross-section of a sensor on a capacitive-touch screen along with capacitances on the capacitive-touch screen. (Prior Art)

FIG. 2 is a layout of a capacitive-touch screen indicating the locations of the electrodes. (Prior Art)

FIG. 3 is a graph of change in capacitance in a sensor as result of two fingers making contact with a capacitive-touch screen. (Prior Art)

FIG. 4 a is a schematic diagram of a voltage source charging a capacitor. (Prior Art)

FIG. 4 b is a schematic diagram of a charged capacitor and an uncharged capacitor. (Prior Art)

FIG. 4 c is a schematic diagram of a charge being transferred from one capacitor to another capacitor. (Prior Art)

FIG. 5 is a schematic diagram of a charge transfer circuit. (Prior Art)

FIG. 6 is a schematic drawing of an apparatus for determining the location(s) of objects making contact with a capacitive-touch screen. (Prior Art)

FIG. 7 illustrates a large sensor spacing topology according to an embodiment of the invention.

FIG. 8 illustrates recovery of the change in capacitance with a large sensor spacing topology according to an embodiment of the invention.

FIG. 9 illustrates recovery of the change in capacitance with a small sensor spacing topology according to an embodiment of the invention.

FIG. 10 is a flow chart illustrating a method of determining the location(s) of contact made with a capacitance touch screen according to an embodiment of the invention.

DETAILED DESCRIPTION

The drawings and description, in general, disclose a method and apparatus for detecting the position(s) where sensor(s) are activated on an interactive screen using sparse-activation compressive sensing. Sparse-activation compressive sensing, in an embodiment of this invention, makes use of the situation where the number of simultaneously activated sensors (e.g. 10 or less per person) is substantially smaller than the number of sensors (nodes) (e.g. 100 s). Because the number of simultaneously activated sensors is substantially smaller than the number of sensors, the number of measurements required for determining which sensors are activated may also be reduced. Because fewer measurements are required when compared with full-scan techniques, less circuitry and power is required to detect the location(s) of activated sensors on an interactive screen.

An embodiment of the invention for determining where activated sensors on an interactive screen are located includes three steps. During a first step, the sensors in a column of N sensors are driven to initial states. The initial states are chosen to simplify the sparse-activation compressive sensing algorithm used as part of this embodiment. The states of the N sensors are a function of the initial state and interaction(s) they sense. Also during the first step, the outputs from the N sensors are combined into a single state. After the N sensors are summed into a single state, the single state is electronically stored.

During a second step of this embodiment of the invention, the first step is repeated K times. The number of times K the first step is repeated is substantially smaller than the number of sensors N. During a third step of this embodiment, the locations of where the sensors are activated on the interactive screen are determined using the K electronically stored single states and sparse-activation compressive sensing.

In another embodiment of the invention, voltage drivers pre-charge sensors (nodes) in a column to distinct voltages. After the sensors in the column have been pre-charged to distinct voltages V_(n), the sensors are electrically connected in parallel and charge from these sensors is transferred to a reference capacitor C_(ref). The charge on the reference capacitor C_(ref) is converted to a sensed voltage V_(sense) by a capacitance-to-voltage converter. The sensed voltage V_(sense) is stored in a touch-screen controller. The process of 1) pre-charging the sensors in a column to voltage V_(n), 2) connecting the sensors in parallel, 3) transferring charge from the sensors to a reference capacitor C_(ref), 4) converting the charge on the reference capacitor C_(ref) to a sensed voltage V_(sense), and 5) storing the sensed voltage V_(sense) in a touch-screen controller is repeated K times (where the value of K is significantly smaller than the number of sensors N−1) in order to create a linear equation where the change in capacitance of any of the sensors can be determined using sparse-activation compressive sensing.

The linear equation and sparse-activation compressing sensing along with other embodiments of the invention will be discussed in more detail later in the specification.

FIG. 1 is a diagram showing a cross-section of a sensor 112 on a capacitive-touch screen 100 along with capacitances on a capacitive-touch screen 100. Two layers of indium tin dioxide (ITO) electrodes 102 and 104 are laid over an LCD screen 108. A layer of dielectric material (e.g. plastic or pyrex glass) 106 is located between the two layers of electrodes 102 and 104.

Consider a capacitive-touch screen as show in FIG. 2 with M row electrodes RE[0]-RE[M−1] and N column electrodes CE[0]-CE[N−1]. The capacitive-touch screen shown in FIG. 2 has M×N capacitance sensors S_(0,0)-S_([M-1],[N-1]) (nodes) where each sensor has a parasitic capacitance C at the intersection of each column and row electrode. The intersection of each column and row electrode is denoted with a dashed square in FIG. 2. At the intersection of column and row electrodes, electrodes are not directly connected (i.e. they are not shorted to each other). A finger 110 (other objects other than a finger may be used such as a stylus) close to a sensor shunts a portion of the electrical field to ground, which is equivalent to adding a capacitance ΔC in parallel with C. Therefore, the sensed capacitance on the node becomes:

C= C+ΔC.  equ. 1)

Each sensor S_(0,0)-S_([M-1],[N-1]) on the capacitive-touch screen 200 can be viewed as a pixel in an image. After calibrating out of C, the remaining ΔC on each node effectively constitutes a two dimensional image of touches or contact made with the capacitive-touch screen 200. Touches may be detected as peaks in the image with properties such as finger size, shape, orientation and pressure as reflected in the shapes of the peaks. When there are a small number of fingers relative to the number of sensors on the capacitive-touch screen, the image is considered to be sparse. As a result of the image being sparse, sparse-activation compressive sensing techniques may be used to determine where on the capacitive-touch screen an object, such as a finger, is located.

FIG. 3 is a graph of change in capacitance on a sensor as result of two fingers making contact with a capacitive-touch screen. FIG. 3 illustrates that the capacitance of a sensor changes where contact is made with the two fingers (i.e. active nodes). In this example, the number of untouched sensors (i.e. inactive nodes) is significantly greater than the number of touched sensors (i.e. active nodes). Because the simultaneous touches on the capacitive-touch screen is sparse, the complexity of sensing the touches may be reduced while maintaining the accuracy of detection and localization.

FIGS. 4 a-4 c are schematic diagrams of a charge transfer technique. As shown in FIGS. 4 a-4 c, the charge transfer is realized in two stages: the pre-charge stage and the transfer stage. In the pre-charge stage as shown in FIG. 4 a, the capacitor C is charged with a known voltage source V_(drive) such that in the steady state the charge Q is equal to Q=(V_(drive)*C) as shown in FIG. 4 b. In the transfer stage, FIG. 4 c, a reference capacitor C_(ref) is connected in parallel with C such that charge on C is transferred onto C_(ref): The voltage on C_(ref) is V_(sense). According to law of conservation of total charge, we have:

V _(drive) *C=V _(sense)(C+C _(ref))  equ. 2)

which can be rearranged as:

V _(sense) =C/(C+C _(ref))*V _(dnve)  equ. 3)

In this case because C_(ref)>>C, we have:

V _(sense)=(C/C _(ref))*V _(drive)  equ. 4)

Equation 4 makes it possible to estimate the capacitance of a sensor C as a proportional relationship between the drive voltage V_(drive), the sense voltage V_(sense) and reference capacitance C_(ref). In this embodiment of the invention, this relationship is used, along with others, to determine where contact is made on a capacitive-touch screen.

An alternative method for using charge transfer to determine the capacitance of a sensor is shown in FIG. 5. An operational amplifier 502 is utilized and the polarity of V_(sense) is inverted. This method for using charge transfer to determine the capacitance of a sensor also provides a proportionality relationship between the drive voltage V_(drive), the sense voltage V_(sense) and capacitance C:

V _(sense) =gCV _(drive) wherein g is a constant.  equ. 5)

FIG. 6 is a schematic drawing of an apparatus for determining the location(s) of objects making contact with a capacitive-touch screen 602. In this embodiment, voltage drivers VD[0]-VD[M−1] drive each sensor S in an individual column n selected from columns C[0]-CE[N−1] to a distinctive voltage during a pre-charge stage through row electrodes RE[0]-RE[M−1]. In this embodiment, each sensor S in a column n is charged by driving the row electrodes RE[0]-RE[M−1] to a positive voltage V_(drive) while the column electrodes C[0]-CE[N−1] are grounded. However, in other embodiments the column electrodes C[0]-CE[N−1] may be driven to non-zero voltages.

In the transfer stage, all the sensors of the selected column n are connected in parallel and the charge accumulated over all the sensors in the selected column n is transferred onto a reference capacitor C_(ref) to induce a sensed voltage V_(sense). The capacitance-to-voltage converter 604 may use the techniques shown in FIGS. 4 a-4 c, FIG. 5 or other techniques known in the art to convert the capacitance to the sensed voltage V_(sense). The sensed voltage V_(sense) is stored in the touch-screen controller 606 where it is used later.

The pre-charge stage and the transfer stage are repeated K times, each time with a distinctive set of voltages. The driving voltage at row m for column n during the k-th (k=0, 1, 2 . . . K−1) pre-charge stage is V_(m,n) ^(k). The sensed voltage is equal to:

$\begin{matrix} {v_{n}^{k} = {{gQ} = {g{\sum\limits_{m = 1}^{M}{C_{m,n}{V_{m,n}^{k}.}}}}}} & \left. {{equ}.\mspace{14mu} 6} \right) \end{matrix}$

where g is a constant, Q is the total charge and C_(m,n) is the node capacitance of a sensor S at the intersection of row m (m=0, . . . , M−1) and column n. After the pre-charge stage and transfer stage have been repeated K times, the K stored voltage measurements can be combined into the following linear equation:

$\begin{matrix} {\begin{bmatrix} v_{n}^{0} \\ \vdots \\ v_{n}^{K - 1} \end{bmatrix} = {{{g\begin{bmatrix} V_{0,n}^{0} & \ldots & V_{{M - 1},n}^{0} \\ \vdots & \ddots & \vdots \\ V_{0,n}^{K - 1} & \ldots & V_{{M - 1},n}^{K - 1} \end{bmatrix}}\begin{bmatrix} C_{0,n} \\ \vdots \\ C_{{M - 1},n} \end{bmatrix}}.}} & \left. {{equ}.\mspace{14mu} 7} \right) \end{matrix}$

Equation 7) above may be written in matrix form (ignoring the proportionality constant g) and given below by the following equation:

v _(n)=Φ_(n) C _(n)  equ. 8)

with the following definitions for the following vectors:

v _(n) =[v _(n) ⁰ . . . v _(n) ^(K−1)]^(T),

C _(n) [C _(0,n) . . . C _(M-1,n)]^(T),

and the pre-charge matrix:

$\Phi_{n} = {\begin{bmatrix} V_{0,n}^{0} & \ldots & V_{{M - 1},n}^{0} \\ \vdots & \ddots & \vdots \\ V_{0,n}^{K - 1} & \ldots & V_{{M - 1},n}^{K - 1} \end{bmatrix}.}$

Generally speaking, it is impossible to uniquely recover C_(n) (the capacitance on a sensor) from V_(n) if K<M due to the system of equations being under-determined. However, when the solution is sparse, C_(n) can be uniquely resolved using sparse-activation compressive sensing. In order for the solution to be sparse, the number of touches on the screen must be substantially smaller than the number of sensors (nodes) on the screen. This assumption may also be extended to each column of sensors when only a small number of sensors on each column are touched simultaneously.

When contact is made with a capacitive-touch screen, the capacitance C_(n) changes. As previously discussed, contact with a capacitive-touch screen creates a capacitance ΔC_(n) in parallel with the parasitic capacitance C _(n) of the sensor S. Therefore the change in capacitance of a sensor is given by:

Δc _(n) =c _(n) − c _(n),  Equ. 9)

Where the parasitic capacitance of a column n is given by:

c _(n) =[ C _(0,n) . . . C _(M-1,n)]^(T),  Equ. 10)

ΔC_(r), is sparse because there are only a small number of non-zero entries in ΔC_(n) (i.e. very few sensors are touched so there are very few changes in capacitance in sensors relative to the number of sensors on a capacitive-touch screen). Combining equations 8) with equation 9), rearranging terms and defining v_(n) ^(c) as the calibrated voltage measurements for column n the following equation is obtained:

v _(n) ^(c) =v _(n)−Φ_(n) c _(n)=Φ_(n) Δc _(n)  Equ. 11)

for the case of perfect calibration and

v _(n) ^(c)=Φ_(n) Δc _(n) +e _(n)  Equ. 12)

for the case of calibration error e_(n).

The change in capacitance ΔCn of sensors in a column can be determined from equation 12 using sparse-activation compressive sensing. For example, when Φ_(n) is a random Gaussian or Bernoulli matrix and ΔCn has a sparsity of s, with K=O(s*log(M/s) (O means “Order of”,—it's a measure of complexity), the change in ΔC_(n) can be uniquely recovered by solving the following equation:

min∥Δc _(n)∥₁

such that

∥v _(n) ^(c)−Φ_(n) Δc _(n)∥₂≦∈,  Equ. 13)

where ∈ is a bound for the calibration error.

In practice, it may be difficult or costly to implement Φ_(n) as a random Gaussian or Bernoulli matrix. Toeplitz or circulant matrices may also be used to implement Φ_(n). Moreover, Toeplitz and circulant matrices may be more easily realized in hardware circuits (e.g. by performing a circular convolution with a random sequence. Toeplitz and circulant matrices may also allow faster decoding.

In the case where the distance between each sensor (node) is much larger than the size of touching objects (e.g. fingers), a touch object could only induce capacitance changes in sensors in close vicinity of the touch. For this case C_(n) is sparse and can be recovered according to equation 13. FIG. 7 illustrates a large sensor spacing topology according to an embodiment of the invention. Each entry in the pre-charge matrix Φ_(n) follows a random Bernoulli distribution such that each sensor (node) is randomly charged with {+V, −V} voltages. FIG. 8 illustrates recovery of the change in capacitance ΔC_(n) with a large sensor spacing topology according to an embodiment of the invention. In this example the compression ratio (WIC) is 8:1 (i.e. M=256 and K=32).

In the case where the distance between each node is small compared with the size of the touching object, multiple sensors are influenced by a single touch and ΔC_(n) is not sparse in its current form. To find a solution for this case, a sparsifying basis ψ is needed such that the projection α_(n) of ΔC_(n) under ψ is sparse. Modifying the recovery algorithm in equation 13 to include the sparsifying basis ψ provides the following:

min∥α_(n)∥₁

such that

∥v _(n) ^(c)−Φ_(n)ψα_(n)∥₂ ≦∈ Δc _(n)=ψα_(n).  equ. 14)

FIG. 9 illustrates recovery of the change in capacitance with a small sensor spacing topology according to an embodiment of the invention. The embodiment show in FIG. 9 uses a DFT (discrete Fourier transform) matrix as the sparsifying matrix ψ. In this example the compression ratio (M/K) is 8:1 (i.e. M=256 and K=32).

For other embodiments of the invention, other sparsifying basis ψ may be used. For example DFT, DCT (discrete cosine transform), wavelet (a wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero), curvelet (curvelets are a non-adaptive technique for multi-scale object representation) may be used as a sparsifying basis ψ. When the sparsifying basis ψ is determined, the pre-charge matrix Φ_(n) can be further optimized to minimize the mutual coherence between Φ_(n) and ψ. As a result, the number of minimally required measurements may be further reduced.

In general, two classes of algorithms may be used to solve the constrained optimization problems in equations 13) and 14). For equation 13), linear/convex optimization may be used. For equation 14) greedy algorithms may be used. Greedy algorithms are often used for hardware realization due to their computational simplicity. For this specific problem, two additional characteristics of ΔC_(n) can be taken advantage of. First, the non-negative assumption of ΔC_(n) leads to a variant of the matching pursuit algorithm that is guaranteed to find a sparse solution when Φ_(n) is properly designed. Second, for small to medium sensor spacing topologies, the non-zero entries in ΔC_(n) are clustered in the vicinity of the touch points instead of sporadically. Model-based compressive sensing theory may be applied to enhance the recovery algorithm according to this block-wise sparsity characteristic.

The column-wise compressive sparse touch shown in FIG. 6 can be extended to a grid sensing scheme. In a grid sensing scheme, all sensors (nodes) S_([0,0])−S_([M-1],[N-1]) on the capacitive-touch screen 602 are driven by voltage drivers VD[0]-VD[M−1] to a distinct voltage during the pre-charge stage. During the transfer stage, all sensors S_([0,0])-S_([M-1],[N-1]) are connected in parallel such the changes accumulated over each individual sensor are mixed together and transferred onto a reference capacitor C_(ref) to derive a sensed voltage V_(sense). The pre-charge stage and the transfer stage are repeated K times, similar to the column-wise compressive sparse touch embodiment, such that the change in capacitance Δc on the sensors due to contact being made with the capacitive-touch screen is determined.

The grid sensing scheme is able to take further advantage of the relative sparsity of active contact made with the capacitive-touch screen 602 compared with the total number of sensors S_([0,0])-S_([M-1],[N-1]). Therefore, the total number of measurements is minimized given the same maximum active touch points assumption discussed previously.

FIG. 10 is a flow chart illustrating a method of determining the location(s) of contact made with a capacitance touch screen according to an embodiment of the invention. During step 1002, each sensor in a column is pre-charged to a distinct voltage Vdrive by voltage drivers VD[0]-VD[M−1]. After the sensors in the column have been pre-charge to a distinct voltage Vdrive, the sensors are electrically connected in parallel as shown in step 1004. During step 1006, charge from all the sensors (node) that are connected in parallel is transferred to a reference capacitor C_(ref). During step 1008, the charge on the capacitor C_(ref) is converted to a sensed voltage, V_(sense). The sensed voltage V_(sense) is stored in a touch-screen controller 606 during step 1010.

When steps 1002-1010 are repeated K (the value of K is substantially smaller than the number of sensors in a column) times, step 1012 proceeds to step 1014. When steps 1002-1010 have not been repeated K times, step 1002 is started again. During step 1014, a value for the change in capacitance ΔC_(n) is determined by solving equation 8) using compressing sensing. The location(s) where contact is made with the capacitive-touch screen is determined using the non-zero value change in capacitance ΔC_(n) of the sensors during step 1016.

The foregoing description has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed, and other modifications and variations may be possible in light of the above teachings. The embodiments were chosen and described in order to best explain the applicable principles and their practical application to thereby enable others skilled in the art to best utilize various embodiments and various modifications as are suited to the particular use contemplated. It is intended that the appended claims be construed to include other alternative embodiments except insofar as limited by the prior art. 

What is claimed is:
 1. A non-transitory machine-implemented method of determining where activated sensors are located on an interactive screen comprising: a first step, the first step comprising: applying an initial state to each sensor in a group of N sensors; wherein states of the N sensors are a function of the initial state and an interaction they sense; combining outputs from the N sensors to a single state; storing the single state; a second step, the second step comprising: repeating the first step K times; wherein the value of K is substantially less than the number of sensors N; a third step, the third step comprising: determining the location(s) where sensors are activated on the interactive screen using the K stored states and sparse-activation compressive sensing.
 2. The method of claim 1 wherein the group of N sensors are arranged in a column or a grid.
 3. The method of claim 1 wherein the interaction that is sensed is touch.
 4. The method of claim 1 wherein the sensors are used to measure capacitance.
 5. The method of claim 1 wherein the initial state is chosen to simplify the sparse-activation compressive sensing algorithm.
 6. The method of claim 1 wherein the sparse-activation compressive sensing is a linear/convex optimization or a greedy algorithm.
 7. The method of claim 1 wherein a sparsifying basis is used in the sparse-activation compressive sensing.
 8. The method of claim 7 wherein the sparsifying basis is selected from a group consisting of a DFT, a DCT, a wavelet and a curvelet.
 9. The method of claim 4 wherein the interactive screen is a capacitive-touch screen; wherein applying an initial state to each sensor in a group of N sensors comprises: precharging each sensor in the group of N sensors to a distinct voltage V_(n); wherein combining the outputs from the N sensors to a single state comprises: electrically connecting all N sensors in parallel; transferring charge from all N sensors connected in parallel to a reference capacitor C_(ref); converting the charge transferred to the reference capacitor C_(ref) to a sensed voltage V_(sense); wherein the sensed voltage V_(sense) equals the single state; wherein determining the location(s) where sensors are activated on the interactive screen using the K stored states and sparse-activation compressive sensing comprises: determining a capacitance C_(n) for each sensor in the column of N sensors by solving an equation using sparse-activation compressive sensing, the equation given by: v_(n) = Φ_(n)c_(n) wherein $\Phi_{n} = \begin{bmatrix} V_{0,n}^{0} & \ldots & V_{{M - 1},n}^{0} \\ \vdots & \ddots & \vdots \\ V_{0,n}^{K - 1} & \ldots & V_{{M - 1},n}^{K - 1} \end{bmatrix}$ $c_{n} = \begin{bmatrix} C_{0,n} & \ldots & C_{{M - 1},n} \end{bmatrix}^{T}$ wherein C_(m,n) is the node capacitance of a sensor at the intersection of row m and column n; wherein m=(0, 1 . . . , M−1); wherein an activated sensor on the capacitive-touch screen is located where the capacitance C_(m,n) of sensor(s) is different from the capacitance of sensors that are not activated on the capacitive-touch screen.
 10. The non-transitory machine-implemented method of claim 9 wherein parasitic capacitance of the N sensors in the column is given by: c _(n) =[ C _(0,n) . . . C _(M-1,n)]^(T) wherein change in capacitance at a sensor is given by: Δc _(n) =c _(n) − c _(n). wherein the number of non-zero values for ΔC_(n) is substantially fewer than the number of N sensors; wherein a calibrated voltage v_(n) ^(c) is equal to: v _(n) ^(c)=Φ_(n) Δc _(n) +e _(n) wherein e_(n) is calibration error; wherein ΔC_(n) is determined by solving the following equation: min∥Δc _(n)∥₁ such that ∥v _(n) ^(c)−Φ_(n) Δc _(n)∥₂≦∈ wherein ΔC_(n) has a sparsity s with K=O(s*log(M/s)).
 11. An apparatus for determining where activated sensors on an interactive screen are located comprising: a first electronic circuit, wherein the first electronic circuit applies an initial state to each sensor in a group of N sensors; wherein states of the N sensors are a function of the initial state and an interaction they sense; a second electronic circuit, wherein the second electronic circuit sums outputs from the N sensors to a single state and stores the single state; a third electronic circuit, wherein the third electronic circuit controls the first and second electronic circuits such that the N sensors are driven to initial states K times and the single state is stored K times; wherein the value of K is substantially less than the number of sensors N; wherein the third electronic circuit determines the location(s) where sensors are activated on the interactive screen using the K stored single states and sparse-activation compressive sensing.
 12. The apparatus of claim 11 wherein the group of N sensors are arranged in a column or a grid.
 13. The apparatus of claim 11 wherein the interaction that is sensed is touch.
 14. The apparatus of claim 11 wherein the sensors are used to measure capacitance.
 15. The apparatus of claim 11 wherein the initial state is chosen to simplify the sparse-activation compressive sensing algorithm.
 16. The apparatus of claim 11 wherein the sparse-activation compressive sensing is a linear/convex optimization or a greedy algorithm.
 17. The apparatus of claim 11 wherein a sparsifying basis is used in the sparse-activation compressive sensing.
 18. The apparatus of claim 17 wherein the sparsifying basis is selected from a group consisting of a DFT, a DCT, a wavelet and a curvelet. 